论文标题
量子步行中的互补性
Complementarity in quantum walks
论文作者
论文摘要
我们研究具有位置和硬币依赖相移的$ D $ CYCLE的离散时间量子步行。这样的模型模拟了带有人造量规场在环上移动的量子粒子的动力学。在我们的情况下，相移的幅度受单个离散参数$ q $管状。我们通过分析方法解决该模型，并观察到，对于Prime $ d $，在两个量子步行进化运营商的特征向量之间存在着强大的互补性，这些量子在$ 2D $尺寸的Hilbert Space中起作用。也就是说，如果$ d $是素数，则进化运算符的相应特征向量遵守$ | \ langle v_q | v'_ {q'} \ rangle | \ leq 1/\ sqrt {d} $ for $ q \ neq q'$，对于所有$ | v_q \ rangle $和$ | v'_ {q'} \ rangle $。我们还讨论了这种互补性的动态后果。最后，我们表明互补性仍然存在于该模型的连续版本中，该版本对应于一维的狄拉克粒子。
We study discrete-time quantum walks on $d$-cycles with a position and coin-dependent phase-shift. Such a model simulates a dynamics of a quantum particle moving on a ring with an artificial gauge field. In our case the amplitude of the phase-shift is governed by a single discrete parameter $q$. We solve the model analytically and observe that for prime $d$ there exists a strong complementarity property between the eigenvectors of two quantum walk evolution operators that act in the $2d$-dimensional Hilbert space. Namely, if $d$ is prime the corresponding eigenvectors of the evolution operators obey $|\langle v_q|v'_{q'} \rangle| \leq 1/\sqrt{d}$ for $q\neq q'$ and for all $|v_q\rangle$ and $|v'_{q'}\rangle$. We also discuss dynamical consequences of this complementarity. Finally, we show that the complementarity is still present in the continuous version of this model, which corresponds to a one-dimensional Dirac particle.
